Do you sue or does your RKBA nucleus in your noggin say that you should NOT sue for the cause? Do you eat the costs and disability even though one could argue that the GG should not have pursued even though the BG got 'what he deserved' and it showed that we stand up to crime, etc.
Yes, I would sue. The shooter is liable for every shot they fire. The GG chased the BG and fired shots, even though the BG no longer posed a threat. Obviously, with the BG running, if he was to be shot, it would be in the back. If you were hit, as a result of reckless behavior by the GG, and severely injured, then yes, you should sue. I have a feeling any sensible jury would agree.
The prosecutor would paint a picture of the GG as being reckless and needlessly endangering peoples lives. The BG was running and being shot at, and in the process you were hit. The prosecutor would say that it is the job of the police to investigate and arrest criminals, not the job of the "average joe" to gun down criminals like it's the wild west.
I don't agree with all of that, but that is likely what would happen. If you were seriously injured, medical bills would mount quickly. If you were disabled, unable to work, and had a family to support, that leaves you in a very bad position. How else, if unable to work, would you support your family, let alone try to pay the extremely high cost of medical care these days?